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Simplifying
(4x + -1y)(4x + y) = 0
Multiply (4x + -1y) * (4x + y)
(4x * (4x + y) + -1y * (4x + y)) = 0
((4x * 4x + y * 4x) + -1y * (4x + y)) = 0
Reorder the terms:
((4xy + 16x2) + -1y * (4x + y)) = 0
((4xy + 16x2) + -1y * (4x + y)) = 0
(4xy + 16x2 + (4x * -1y + y * -1y)) = 0
(4xy + 16x2 + (-4xy + -1y2)) = 0
Reorder the terms:
(4xy + -4xy + 16x2 + -1y2) = 0
Combine like terms: 4xy + -4xy = 0
(0 + 16x2 + -1y2) = 0
(16x2 + -1y2) = 0
Solving
16x2 + -1y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y2' to each side of the equation.
16x2 + -1y2 + y2 = 0 + y2
Combine like terms: -1y2 + y2 = 0
16x2 + 0 = 0 + y2
16x2 = 0 + y2
Remove the zero:
16x2 = y2
Divide each side by '16'.
x2 = 0.0625y2
Simplifying
x2 = 0.0625y2
Take the square root of each side:
x = {-0.25y, 0.25y}
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